Question: Given $ m \angle RPS = 9x - 3$, $ m \angle QPR = 3x + 13$, and $ m \angle QPS = 70$, find $m\angle RPS$. $P$ $Q$ $S$ $R$
Explanation: From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Substitute in the expressions that were given for each measure: $ {3x + 13} + {9x - 3} = {70}$ Combine like terms: $ 12x + 10 = 70$ Subtract $10$ from both sides: $ 12x = 60$ Divide both sides by $12$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $m\angle RPS$ $ m\angle RPS = 9({5}) - 3$ Simplify: $ {m\angle RPS = 45 - 3}$ So ${m\angle RPS = 42}$.